arXiv subjects

Claudio De Persis

Publications and source records attributed to Claudio De Persis.

At least 19 recordsLinked to original sources

arXiv2026

Machines that Predict Trajectories from Templates

We study trajectory prediction from libraries of stored output templates. Given the past of an unknown trajectory, the goal is to predict its future without identifying the state-space model that generated it. We show that libraries of trajectories generated by one or more dynamical systems define behavioral spaces that can be used as prediction mechanisms. For linear systems, we characterize exact prediction in terms of continuation maps, behavioral containment, and spectral conditions on output-visible eigenvalues. We also analyze robustness to noisy observations and noisy libraries, derive error bounds for out-of-library trajectories, and show how interconnection constraints can compose template libraries into new behavioral spaces with emergent modes. Finally, we extend the framework to nonlinear systems whose output trajectories are contained in, or immersed into, finite-dimensional linear behaviors. These results provide a theory of template-based prediction machines capable of generalizing beyond the stored trajectories and, in some cases, beyond the systems that generated them.

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arXiv2026

Output regulation via input-output data

From a multi-input-multi-output (MIMO) discrete-time linear system, we collect input-output data affected by noise in the form of an unknown exosignal and, from these data points (without knowledge of the system model), we design a feedback controller that asymptotically annihilates the effect of that exosignal on the output. This amounts to solving an output regulation problem purely from input-output data, for MIMO linear systems. The design of the controller corresponds to a semidefinite program and is pursued on a suitable auxiliary system. Such design carries over from the auxiliary system to the original one by a rigorous examination of the relation between the solutions of the two systems.

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arXiv2025

Event-triggered control of nonlinear systems from data

In a recent paper [8], we introduced a data-based approach to design event-triggered controllers for linear systems directly from data. Here, we extend the results in [8] to a class of nonlinear systems. We provide two data-based designs certified by a (classical) Lyapunov function. For these two designs, we devise event-triggered policies that rely on the previously found Lyapunov function, have parameters tuned from data, ensure a positive minimum inter-event time, and act based either on the state error or on the library error. These two different policies, and their respective advantages, are illustrated numerically.

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arXiv2025

Data-driven stabilization of nonlinear systems via descriptor embedding

We introduce the notion of descriptor embedding for nonlinear systems and use it for the data-driven design of stabilizing controllers. Specifically, we provide sufficient data-dependent LMI conditions which, if feasible, return a stabilizing nonlinear controller of the form $u=K(x)Z(x)$ where $K(x)$ belongs to a polytope and $Z$ is a user-defined function. The proposed method is then extended to account for the presence of uncertainties and noisy data. Furthermore, a method to estimate the resulting region of attraction is given using only data. Simulation examples are used to illustrate the results and compare them to existing methods from the literature.

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arXiv2025

A Versatile Framework for Data-Driven Control of Nonlinear Systems

This note aims to provide a systematic investigation of direct data-driven control, enriching the existing literature not by adding another isolated result, but rather by offering a unifying, versatile, and broad framework that enables the generation of novel results in this domain. We formulate the nonlinear design problem from a high-level perspective as a set of desired controlled systems and propose systematic procedures to synthesize data-driven control algorithms that meet the specified design requirements. Various examples are presented to demonstrate the applicability of the proposed approach and its ability to derive new insights and results, illustrating the novel contributions enabled by the framework.

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arXiv2025

Enforcing contraction via data

We present data-based conditions for enforcing contractivity via feedback control and obtain desired asymptotic properties of the closed-loop system. We focus on unknown nonlinear control systems whose vector fields are expressible via a dictionary of functions and derive data-dependent semidefinite programs whose solution returns the controller that guarantees contractivity. When data are perturbed by disturbances that are linear combinations of sinusoids of known frequencies (but unknown amplitude and phase) and constants, we remarkably obtain conditions for contractivity that do not depend on the magnitude of the disturbances, with imaginable positive consequences for the synthesis of the controller. Finally, we show how to design from data an integral controller for nonlinear systems that achieves constant reference tracking and constant disturbance rejection.

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arXiv2025

Neural network based control of unknown nonlinear systems via contraction analysis

This paper studies the design of neural network (NN)-based controllers for unknown nonlinear systems, using contraction analysis. A Neural Ordinary Differential Equation (NODE) system is constructed by approximating the unknown draft dynamics with a feedforward NN. Incremental sector bounds and contraction theory are applied to the activation functions and the weights of the NN, respectively. It is demonstrated that if the incremental sector bounds and the weights satisfy some non-convex conditions, the NODE system is contractive. To improve computational efficiency, these non-convex conditions are reformulated as convex LMI conditions. Additionally, it is proven that when the NODE system is contractive, the trajectories of the original autonomous system converge to a neighborhood of the unknown equilibrium, with the size of this neighborhood determined by the approximation error. For a single-layer NN, the NODE system is simplified to a continuous-time Hopfield NN. If the NODE system does not satisfy the contraction conditions, an NN-based controller is designed to enforce contractivity. This controller integrates a linear component, which ensures contraction through suitable control gains, and an NN component, which compensates for the NODE system's nonlinearities. This integrated controller guarantees that the trajectories of the original affine system converge to a neighborhood of the unknown equilibrium. The effectiveness of the proposed approach is demonstrated through two illustrative examples.

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arXiv2024

Data-driven harmonic output regulation of a class of nonlinear systems

The paper deals with the data-based design of state-feedback controllers that solve the output regulation problem for a class of nonlinear systems. Inspired by recent developments in model-based output regulation design techniques and in data-driven control design for nonlinear systems, we derive a data-dependent semidefinite program that, when solved, directly returns a controller that steers the regulation error to a periodic signal whose Fourier series has identically zero coefficients up to a certain order set by the controller. When specialized to the case of linear systems, the result appears to improve upon existing work. Numerical results illustrate the findings

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arXiv2024

Data-driven input-to-state stabilization

For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator and process disturbances. We address this problem in a data-based setting when we cannot avail ourselves of the dynamics of the actual system, but only of data generated by it under unknown bounded noise. For all dynamics consistent with data, we derive sum-of-squares programs to design an input-to-state stabilizing controller, an input-to-state Lyapunov function and the corresponding comparison functions. This numerical design for input-to-state stabilization seems to be relevant not only in the considered data-based setting, but also in a model-based setting. Illustration of feasibility of the provided sum-of-squares programs is provided on a numerical example.

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arXiv2024

Controller synthesis for input-state data with measurement errors

We consider the problem of designing a state-feedback controller for a linear system, based only on noisy input-state data. We focus on input-state data corrupted by measurement errors, which, albeit less investigated, are as relevant as process disturbances in applications. For energy and instantaneous bounds on these measurement errors, we derive linear matrix inequalities for controller design where the one for the energy bound is equivalent to robust stabilization of all systems consistent with the noisy data points via a common Lyapunov function.

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arXiv2024

Setpoint control of bilinear systems from noisy data

We consider the problem of designing a controller for an unknown bilinear system using only noisy input-states data points generated by it. The controller should achieve regulation to a given state setpoint and provide a guaranteed basin of attraction. Determining the equilibrium input to achieve that setpoint is not trivial in a data-based setting and we propose the design of a controller in two scenarios. The design takes the form of linear matrix inequalities and is validated numerically for a Cuk converter.

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arXiv2024

Convex Co-Design of Control Barrier Function and Safe Feedback Controller Under Input Constraints

We study the problem of co-designing control barrier functions (CBF) and linear state feedback controllers for continuous-time linear systems. We achieve this by means of a single semi-definite optimization program. Our formulation can handle mixed-relative degree problems without requiring an explicit safe controller. Different L-norm based input limitations can be introduced as convex constraints in the proposed program. We demonstrate our results on an omni-directional car numerical example.

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arXiv2024

Controller Synthesis from Noisy-Input Noisy-Output Data

We consider the problem of synthesizing a dynamic output-feedback controller for a linear system, using solely input-output data corrupted by measurement noise. To handle input-output data, an auxiliary representation of the original system is introduced. By exploiting the structure of the auxiliary system, we design a controller that robustly stabilizes all possible systems consistent with data. Notably, we also provide a novel solution to extend the results to generic multi-input multi-output systems. The findings are illustrated by numerical examples.

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arXiv2023

Data-based Transfer Stabilization in Linear Systems

We present a novel framework for transferring the knowledge from one system (source) to design a stabilizing controller for a second system (target). Our motivation stems from the hypothesis that abundant data can be collected from the source system, whereas the data from the target system is scarce. We consider both cases where data collected from the source system is noiseless and noisy. For each case, by leveraging the data collected from the source system and a priori knowledge on the maximum distance of the two systems, we find a suitable, and relatively small, compact set of systems that contains the actual target system, and then provide a controller that stabilizes the compact set. In particular, the controller can be obtained by solving a set of linear matrix inequalities (LMIs). Feasibility of those LMIs is discussed in details. We complement our theoretical findings by two numerical case studies of low-order and high-order systems.

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arXiv2023

Data-driven control of nonlinear systems from input-output data

The design of controllers from data for nonlinear systems is a challenging problem. In a recent paper, De Persis, Rotulo and Tesi, "Learning controllers from data via approximate nonlinearity cancellation," IEEE Transactions on Automatic Control, 2023, a method to learn controllers that make the closed-loop system stable and dominantly linear was proposed. The approach leads to a simple solution based on data-dependent semidefinite programs. The method uses input-state measurements as data, while in a realistic setup it is more likely that only input-output measurements are available. In this note we report how the design principle of the above mentioned paper can be adjusted to deal with input-output data and obtain dynamic output feedback controllers in a favourable setting.

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arXiv2023

Data-driven input-to-state stabilization with respect to measurement errors

We consider noisy input/state data collected from an experiment on a polynomial input-affine nonlinear system. Motivated by event-triggered control, we provide data-based conditions for input-to-state stability with respect to measurement errors. Such conditions, which take into account all dynamics consistent with data, lead to the design of a feedback controller, an ISS Lyapunov function, and comparison functions ensuring ISS with respect to measurement errors. When solved alternately for two subsets of the decision variables, these conditions become a convex sum-of-squares program. Feasibility of the program is illustrated with a numerical example.

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arXiv2023

Data-driven stabilizer design and closed-loop analysis of general nonlinear systems via Taylor's expansion

For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system can be expressed or well-approximated by the basis functions and the experimental data. For a more general setting where explicit information on the basis functions is not available, this paper presents a data-driven approach for stabilizer design and closed-loop analysis via the Lyapunov method. First, based on Taylor's expansion and using input-state data, a stabilizer and a Lyapunov function are designed to render the known equilibrium locally asymptotically stable. Then, data-driven conditions are derived to check whether a given sublevel set of the found Lyapunov function is an invariant subset of the region of attraction. One of the main challenges is how to handle Taylor's remainder in the design of the local stabilizers and the analysis of the closed-loop performance.

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arXiv2023

Learning controllers from data via kernel-based interpolation

We propose a data-driven control design method for nonlinear systems that builds on kernel-based interpolation. Under some assumptions on the system dynamics, kernel-based functions are built from data and a model of the system, along with deterministic model error bounds, is determined. Then, we derive a controller design method that aims at stabilizing the closed-loop system by cancelling out the system nonlinearities. The proposed method can be implemented using semidefinite programming and returns positively invariant sets for the closed-loop system.

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